In recent years, lithographic technologies for printing integrated circuit patterns on wafers have rapidly been developing. Demand for higher integration densities in integrated circuits has been increased than ever. In order to achieve a higher integration density, it is necessary to improve the resolution of a projection optical system in a projection exposure system. The resolution of a projection lens is dominated by the wavelength of light used therein and the numerical aperture (NA) of the projection lens. In order to improve the resolution, the wavelength of the light to be used is shortened, and the NA of the projection optical system is enlarged (enlargement of aperture).
Wavelengths of light for use in projection exposure systems have been already shortened to g-line (wavelength: 436 nm) or i-line (wavelength: 365 nm). The use of KrF excimer laser light (wavelength: 248 nm), ArF excimer laser light (wavelength: 193 nm), and the like, which have yet shorter wavelengths, has been also examined. As wavelengths of light have been further shortened as described above, multicomponent optical glass, which is commonly used in imaging optical systems such as projection optical systems, cannot be used as material for lenses any longer in terms of transmittance deterioration. Therefore, in optical systems for excimer laser steppers, using quartz glass or fluoride crystals (for example, calcium fluoride (fluorite)) as optical members is common.
It is said that crystal material is preferably a single crystal in order to satisfy optical performance as of an optical member for use in an optical system of an excimer laser stepper. Furthermore, along with the trend toward higher performance of projection exposure systems, calcium fluoride single crystals having a large aperture of approximately φ120 mm to φ350 mm are desired in recent years. A calcium fluoride (fluorite) single crystal has a lower refractive index and a smaller dispersion (wavelength dependency of refractive index) than those of general optical glass, and therefore is very effective in that chromatic aberration can be compensated when used together with an optical member made of other material. Moreover, calcium fluoride single crystals are more available than other fluoride crystals (barium fluoride and the like) in the market, and a large aperture single crystal having a diameter of φ120 mm or more is also available.
Calcium fluoride single crystals having these advantages have been conventionally used as material for lenses of cameras and telescopes in addition to optical material for steppers. Moreover, recently, other than calcium fluoride single crystals, single crystals of barium fluoride and strontium fluoride, which are fluoride single crystals, also belong to the isometric system and are drawing attention as next-generation optical material because of their similar properties.
As a crystal growth method for a fluoride single crystal, a number of melt methods including the Bridgeman method (the Stockbarger method, or the pulling down method) and the Tammann has been known. Herein, it is considered that the growth direction of a fluoride crystal manufactured by the Bridgeman method or the like has no significance. Actually, the horizontal surfaces of obtained ingots show random crystal plane orientations every time a crystal is grown.
After crystal growth, since large residual stresses exist in a taken out ingot, simple heat treatment is usually performed on the ingot as it is. Subsequently, the ingot is cut into appropriate sizes depending on a desired product, and heat treatment for obtaining desired optical performance (homogeneity of refractive index, birefringence, and the like) is performed on the cut-out materials.
In the case where crystal plane directions are not considered, the ingot is cut horizontally (sliced in rounds), thus making it possible to effectively cut out larger materials for fabricating optical elements (lenses or the like) from the ingot.
Moreover, it has been known that the {111} planes of a fluoride single crystal have higher optical performance than that of other crystal planes in the perpendicular direction. Accordingly, in order to obtain a fluoride single crystal having high optical performance, the following method may be adopted. Specifically, in the method, the {111} planes of a fluoride single crystal ingot are measured, a material for fabricating an optical element is cut out so that the {111} planes constitute two parallel flat surfaces, and then heat treatment is performed. Alternatively, the following method may be adopted. Specifically, in the method, heat treatment is performed on an ingot of a fluoride single crystal obtained by crystal growth, and then a material for fabricating an optical element is cut out so that two opposite flat surfaces become {111} planes.
Incidentally, birefringence is a phenomenon in which a refractive index varies depending on the polarization direction of light (electromagnetic wave). In general, birefringence is expressed as an optical path difference (called retardation) when light transmits through a unit length of a substance, and nm/cm is used as a unit thereof. Further, in the case where birefringence is caused by strain, this birefringence is often called strain.
Heretofore, it has been considered that a single crystal in the isometric system, such as calcium fluoride, has no intrinsic birefringence. Further, in the case of a single crystal of calcium fluoride, it has been considered that, even if birefringence is induced by thermal stresses generated in a manufacturing process, the birefringence can be reduced to a level where it does not adversely affect optical design. Actually, for light having a relatively longer wavelength of 633 nm, the value of birefringence has been able to be reduced to approximately 1 to 2 nm/cm by performing predetermined heat treatment.
Under this background, as a method of cutting out optical materials from an ingot, a method in which a phenomenon of crystal cleavage is utilized and the orientation of {111} planes is simply determined has been common. Further, in the case where an optical system is assembled using optical members obtained from the optical materials, the optical members have been arranged in such a manner that the normal of {111} planes is aligned with the optical axis. However, birefringence in crystal plane orientations other than {111} planes has not been considered.